Solid profiles are often formed by pultruding one or more fiber-reinforced ribbons through a die that shapes the ribbons into the desired configuration. The ribbons may include unidirectionally aligned continuous fibers embedded within a polymer matrix. Because the profiles have continuous fibers oriented in the machine direction (longitudinal), they often exhibit good tensile strength in the machine direction. Unfortunately, however, the maximum degree of tensile strength that is achievable is often limited due to the difficulty in processing materials of a very high degree of strength. As such, a need currently exists for a solid profile that exhibits excellent tensile strength, and yet can be made in a relatively efficient and simple manner.